I use "sandpaper" that is not made of sand that is for sanding wood. the "sandpaper" i use is made for metal! I make knives and anyone who does uses a BELT SANDER of some type to form the blade and they use "sandpaper" to finish it as well. The logic i use is very simple get some spray adhesive spray a lil spot near or on your granite slab and stick a piece of 2500 grit "sandpaper" to it then as you work you can strop your tool on this quickly and cleanly and neatly and go on about your business. Now your reason for buying it is the same as mine its cheap and it works and that is what it is made for!
Your stones clog because you dont use a liquid , oil or water or beer or whatever to keep the metal shavings in suspension or you don't clean them off and re apply . All that being said as I stated a few posts ago we are a passionate bunch about sharpening, we all have our ways and they all obviously work so then what is the factor that makes all the different techniques work?????? Practice. Pick one and practice.